Is there a standard way of writing $a$ is divisible by $b$ in mathematical notation?

From what I've search it seems that writing $a \equiv 0 \pmod b$ is one way? But also you can write $b \mid a$ as well (the middle character is a pipe)? And sometimes that pipe is replaced by $3$ vertical dots?

Or is there a way of writing $a$ is a multiple of $b$ which I think means the same thing?

EDIT: thanks for the answers, is there a way to extend this and write something like: $b \mid a$ when $a = k$

@PeterPhipps The spacing is different, compare $A|B$, $A\mid B$, $A\vert B$, $A\lvert B$ and $A\rvert B$ (edit: there actually are differences there in some fonts, even if those are not visible here).
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dtldarekApr 22 '12 at 13:17

Thanks for the list, a mod b = 0 makes the most sense to me. But b|a seems more for use in commentary?
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Jonathan.Apr 22 '12 at 13:19

1

It depends on so many things that I can't tell you this or that way. For me there are three important factors: how often will I use it (more often means less symbols), do I need to use it "in chains" like $a = b = c = d \pmod n$ and do I need to use different $n$-s, e.g. $a \equiv_3 b \equiv_5 c \equiv_7 d$ (which may be confusing but sometimes is helpful). Still, the most important criterion of all is readability.
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dtldarekApr 22 '12 at 13:26

This is the standard way, in the specific meaning of compliance to international standards: ISO 80000-2, clause 2.7-17. Note that the vertical bar character used there is normatively identified as U+2223 DIVIDES (∣), note the common U+007C VERTICAL LINE (|) that we enter directly on a keyboard. It is of course possible to express the same thing using a congruence notation, but only for integers (not e.g. for polynomials).
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Jukka K. KorpelaJun 22 '12 at 5:09